STATISTICAL DISTRIBUTION OF FREQUENCY-RESPONSE IN DISORDERED PERIODIC STRUCTURES

A structure designed to be spatially periodic cannot be exactly periodic. The departure from exact periodicity is known as disorder, and it causes localization of normal modes and additional attenuation of wave motions in the structure not related to damping. The present investigation is directed at a possible adverse effect of disorder, namely, higher structural response near the point at which a dynamic excitation is applied than would occur in a perfectly periodic structure, thereby reducing structure safety and reliability. A systematic procedure is developed herein for the analysis of such an effect for a generic disordered periodic structure. In particular, the probability distribution of structural response is obtained by analysis and by Monte Carlo simulation, which is needed both for fundamental understanding of the effect and for predicting the reliability of a system. It is shown also that, given probability distributions of the disordered parameters of a structure, the mean and standard deviation of structural response can be obtained exactly for a damped randomly disordered periodic structure if the number of disordered cell units is not large and, approximately, if the number is large. Application of the procedure is illustrated by an example, and the results are compared with Monte Carlo simulations.